Article
Reference
Resonance formation in the π
+π
−π
0final state in two-photon collisions
L3 Collaboration
AMBROSI, Giovanni (Collab.), et al.
Abstract
A study of resonance formation is presented in the π⁺π⁻π⁰ final state in two-photon collisions at LEP. The a₂(1320) radiative width is measured to be Γγγ = 0.98 ± 0.05 ± 0.09 keV. The helicity 2 production is dominant. Exclusive π⁺π⁻π⁰ production has also been studied in the mass region above the a₂ in the ϱπ and f2π channels. This region is dominated by a JP = 2⁺
helicity 2 wave.
L3 Collaboration, AMBROSI, Giovanni (Collab.), et al . Resonance formation in the π
+π
−π
0final state in two-photon collisions. Physics Letters. B , 1997, vol. 413, p. 147-158
DOI : 10.1016/S0370-2693(97)01091-5
Available at:
http://archive-ouverte.unige.ch/unige:113031
Disclaimer: layout of this document may differ from the published version.
1 / 1
6 November 1997
PHYSICS LETTERS B ELSEVIER Physics Letters B 413 (1997) 147-158
Resonance formation in the d T- no final state in two-photon collisions
L3 Collaboration
M. Acciarri ab, 0. Adriani q, M. Aguilar-Benitez aa, S. Ahlen k, J. Alcaraz aa, G. Alemanni w, J. Allaby r, A. Aloisio ad, G. Alverson ‘, M.G. Alviggi ad, G. Ambrosi t, H. Anderhub ax, V.P. Andreev am, T. Angelescu m, F. Anselmo i, A. Arefiev ac, T. Azemoon ‘, T. Aziz j, P. Bagnaia ‘, L. Baksay as, R.C. Ball ‘,
S. Banerjee j, SW. Banerjee j, K. Banicz au, A. Barczyk ax,av, R. Barillere r, L. Barone ‘, P. Bartalini ai, A. Baschirotto ab, M. Basile i, R. Battiston ‘, A. Bay w,
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0370-2693/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved.
PIZ SO370-2693(97)01091-S
148 M. Acciarri et al./ Physics Letters B 413 (1997) 147-158
E. Fiandrini ai, J.H. Field t, F. Filthaut aj, P.H. Fisher p, I. Fisk ao, G. Forconi P, L. Fredj t, K. Freudenreich ax, C. Furetta ab, Yu. Galaktionov ac,p, S.N. Ganguli j,
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A. Kopp aw, I. Korolko ac, V. Koutsenko Pyac, R.W. Kraemer q, W. Krenz a, A
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P. Laurikainen “, M. Lebeau r, A. Lebedev p, P. Lebrun ‘, P. Lecomte ax, P. Lecoq r, P. Le Coultre ax, C. Leggett ‘, J.M. Le Goff r, R. Leiste aw, E. Leonardi a1, P. Levtchenko am, C. Li ‘, C.H. Lin az, W.T. Lin =, F.L. Linde b,r, L. Lista ad, Z.A. Liu g, W. Lohmann aw, E. Longo a1, W. Lu *, Y.S. Lu g, K. Libelsmeyer a, C. Luci ‘, D. Luckey p, L. Luminari ‘, W. Lustermann av, W.G. Ma “, M. Maity j, G. Majumder j, L. Malgeri a1, A. Malinin ac, C. Maiia aa, D. Mange01 af, S. Mangla J,
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G. Passaleva 9, S. Patricelli ad, T. Paul ‘, M. Pauluzzi ai, C. Paus a, F. Pauss ax, D. Peach r, Y.J. Pei a, S. Pensotti ab, D. Perret-Gallix d, B. Petersen &, S. Petrak h, A. Pevsner e, D. Piccolo ad, M. Pieri q, J.C. Pinto aj, P.A. Piroue *, E. Pistolesi ab,
V. Plyaskin ac, M. Pohl ax, V. Pojidaev ac7q, H. Postema p, N. Produit t, D. Prokofiev am, G. Rahal-Callot ax, N. Raja J, P.G. Rancoita ab, M. Rattaggi ab,
G. Raven ao, P. Razis ae, K. Read ag, D. Ren ax, M. Rescigno a’, S. Reucroft ‘, T. van Rhee at, S. Riemann aw, K. Riles ‘, 0. Rind ‘, A. Robohm ax, J. Rodin p,
B.P. Roe ‘, L. Romero =, S. Rosier-Lees d, Ph. Rosselet w, W. van Rossum at,
S. Roth a, J.A. Rubio r, D. Ruschmeier h, H. Rykaczewski ax, J. Salicio r,
E. Sanchez aa, M.P. Sanders af, M.E. Sarakinos “, S. Sarkar J, M. Sassowsky a,
M. Acciarri et al/Physics Letters B 413 (1997) 147-158 149
G. Sauvage d, C. Schafer a, V. Schegelsky am, S. Schmidt-Kaerst a, D. Schmitz a, P. Schmitz a, M. Schneegans d, N. Scholz ax, H. Schopper ay, D.J. Schotanus af,
J. Schwenke a, G. Schwering a, C. Sciacca ad, D. Sciarrino t, L. Servoli ai, S. Shevchenko ah, N. Shivarov aq, V. Shoutko ac, J. Shukla y, E. Shumilov ac, A. Shvorob *, T. Siedenburg a, D. Son =, A. Sopczak aw, V. Soulimov ad, B. Smith P,
P. Spillantini q, M. Steuer p, D.P. Stickland *, H. Stone *, B. Stoyanov aq, A. Straessner a, K. Strauch O, K. Sudhakar j, G. Sultanov ‘, L.Z. Sun ‘, G.F. Susinno t, H. Suter a, J.D. Swain ‘, X.W. Tang g, L. Tauscher f, L. Taylor ‘, Samuel C.C. Ting p, S.M. Ting p, M. Tonutti a, S.C. Tonwar j, J. T6th n, C. Tully *, H. Tuchscherer as, K.L. Tung g, Y. Uchida p, J. Ulbricht ax, U. Uwer r, E. Valente a’,
R.T. Van de Walle af, G. Vesztergombi n, I. Vetlitsky ac, G. Viertel ax, M. Vivargent d, R. Viilkert aw, H. Vogel aj, H. Vogt aw, I. Vorobiev ac, A.A. Vorobyov am, A. Vorvolakos ae, M. Wadhwa f, W. Wallraff a, J.C. Wang P, X.L. Wang “, Z.M. Wang ‘, A. Weber a, F. Wittgenstein r, S.X. Wu ‘, S. Wynhoff a,
J. Xu k, Z.Z. Xu “, B.Z. Yang ‘, C.G. Yang g, X.Y. Yao g, J.B. Ye ‘, S.C. Yeh az, J.M. You aj, An. Zalite am, Yu. Zalite am, P. Zemp ax, Y. Zeng a, Z. Zhang g, Z.P. Zhang “, B. Zhou k, Y. Zhou ‘, G.Y. Zhu g, R.Y. Zhu ah, A. Zichichi i*r,s,
F. Ziegler aw
a I. Physikalisches Institut, RW’TH, D-52056 Aachen, FRG ’ III. Physikalisches Institut, RWTH, D-52056 Aachen, FRG 3
b National Institute for High Energy Physics, NIKHEF, and University of Amsterdam, NL-1009 DB Amsterdam, The Netherlands
’ University of Michigan, Ann Arbor, MI 48109, USA
’ Laboratoire d’tlnnecy-le-Vieux de Physique des Particules, LAPP,IN2P3-CNRS, BP 110, F-74941 Annecy-le-Vieux CEDEX, France e Johns Hopkins University, Baltimore, MD 21218, USA
f Institute of Physics, University of Basel, CH-4056 Basel, Switzerland g Institute of High Energy Physics, IHEPs 100039 Beijing, China 4
h Humboldt University, D-10099 Berlin, FRG 3
i University of Bologna and INFN-Sezione di Bologna, I-40126 Bologna, Italy
’ Tata Institute of Fun&mental Research, Bombay 400 005, India k Boston University, Boston, MA 02215, USA
’ Northeastern University, Boston, MA 0211.5, USA
m Institute of Atomic Physics and University of Bucharest, R-76900 Bucharest, Romania
n Central Research Institute for Physics of the Hungarian Academy of Sciences, H-1525 Budapest 114, Hungary 5
’ Harvard University, Cambridge, MA 02139, USA
’ Massachusetts Institute of Technology, Cambridge, MA 02139, USA
’ INFN Sezione di Firenze and University of Florence, I-50125 Florence, Italy r European Laboratory for Particle Physics. CERN, CH-1211 Geneva 23, Switzerland
’ World Laboratory, FBLJA Project, CH-1211 Geneva 23, Switzerland
’ University of Geneva, CH-I211 Geneva 4, Switzerland
’ Chinese University of Science and Technology, USTC, Hefei, Anhui 230 029, China 4
’ SEFT Research Institute for High Energy Physics, P.O. Box 9, SF-00014 Helsinki, Finland w University of Lausanne, CH-IO15 Lausanne, Switzerland
’ INFN-Sezione di Lecce and Universitci Degli Studi di Lecce, I-73100 Lecce, Italy
’ Los Alamos National Laboratory, Los Alamos, NM 87544, USA
’ Institut de Physique Nucleaire de Lyon, IN2P3-CNRSUniversite Claude Bernard, F-69622 Villeurbanne, France aa Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas, CIEMAT E-28040 Madrid, Spain 6
* INFN-Sezione di Milano, I-20133 Milan, Italy
ac Institute of Theoretical and Experimental Physics, ITEP, Moscow, Russia
1.50 M. Acciarri et al./Physics Letters B 413 (19971 147-158 a’ INFN-Sezione di Napoii and University of Naples, l-80125 Naples, Italy
ae Department of Natural Sciences, University of Cyprus, Nicosia, Cyprus af University of Nijmegen and NIKHEF, NL-6525 ED Nijmegen, The Netherlands
ag Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA ah California Institute of Technology, Pasadena, CA 91125, USA
ai INFN-Sezione di Perugia and Universitci Degli Studi di Perugia, I-06100 Perugia, Italy aJ Carnegie Mellon University Pittsburgh, PA 15213, USA
ak Princeton University, Princeton, NJ 08544, USA
al INFN-Sezione di Roma and Uniuersity of Rome, “Lo Sapienza”. I-00185 Rome. Italy am Nuclear Physics Institute, St. Petersburg, Russia
an University and INFN, Salerno, I-84100 Salerno, Italy an University of California, San Diego, CA 92093, USA
ap Dept. de Fisica de Particulas Elementales, Univ. de Santiago, E-15706 Santiago de Compostela, Spain aq Bulgarian Academy of Sciences, Central Lab. of Mechatronics and Instrumentation, BU-Ii13 Sofia, Bulgaria
ar Center for High Energy Physics, Korea Adu. Inst. of Sciences and Technology, 305-701 Taejon. South Korea as University of Alabama, Tuscaloosa, AL 35486, USA
at Utrecht University and NIKHEFs NL-3584 CB Utrecht, The Netherlands au Purdue University, West Lafayette, IN 47907, USA a’ Paul Scherrer Institut, PSI, CH-5232 Villigen, Switzerland aw DESY-lnstitutfir Hochenergiephysik, D-15738 Zeuthen. FRG
” Eidgenijssische Technische Hochschule, ETH Ziirich, CH-8093 Ziirich, Switzerland ay University of Hamburg, D-22761 Hamburg, FRG
az High Energy Physics Group, Taiwan, ROC Received 13 June 1997
Editor: K. Winter
Abstract
A study of resonance formation is presented in the rr’ 7~~ rr ’ final state in two-photon collisions at LEP. The a,(1320) radiative width is measured to be I& = 0.98 f 0.05 5 0.09 keV. The helicity 2 production is dominant. Exclusive n-+ P- rr”
production has also been studied in the mass region above the a2 in the pr and f2~ channels. This region is dominated by a Jp = 2+ helicity 2 wave. 0 1997 Elsevier Science B.V.
1. Introduction
A study of rTT+ r- 7~ a production in two-photon collisions is presented using data taken from 1991 to 1995 by the L3 experiment [l] at a center-of-mass energy = 91 GeV. The corresponding integrated luminosity is 140.6 pb-‘. The previous measure- ments of this process [2-91 have focused on the formation of the ~~(1320) meson with well estab-
lished quantum numbers Jpc = 2++ decaying domi- nantly into p7r. In addition the Crystal Ball [lo] and CELLO [7] collaborations have reported the forma- tion of the ~~(1670) meson (Crystal Ball in the
7r07rorro channel). The 7rTT2 meson is a 2-+ tensor state in the qS model. A nonrelativistic quark-model calculation [l l] predicts a radiative width two to three orders of magnitude smaller than those re- ported (r,, = 1.35 f 0.26 keV [ 121, average of
’ Also supported by CONICET and Universidad National de 4 Supported by the National Natural Science Foundation of
La Plata, CC 67, 1900 La Plata, Argentina. China.
* Also supported by Panjab University, Chandigarh-160014, ’ Supported by the Hungarian OTKA fund under contract num-
India. bers Tl4459 and T24011.
3 Supported by the German Bundesministerium ftir Bildung, 6 Supported also by the Comisi6n Interministetial de Ciencia y
Wissenschaft, Forschung und Technologie. Technologia.
M. Acciarri et al./ Physics Letters B 413 (1997) 147-158 151
Crystal Ball and CELLO measurements). Calcula- tions of relativistic quark-models for two-photon de- cays of mesons [ 13,141 also predict a width an order of magnitude lower. A recent partial wave analysis of the 7~+ r- T’ system from ARGUS [9] has found no evidence of Jp = 22pn and fir states, with an upper limit of &(n,) < 0.19 keV (90% C.L.).
In e+e- storage ring experiments the cross sec- tion for resonance formation in untagged two-photon collisions can be formulated as the product of the two-photon luminosity function
[151 that describes the flux of transverse photons and the resonance cross section given by the Breit-Wigner formula. The 7~+ r- 7~ ’ final state can be expressed as a set of two body intermediate states with orbital angular momentum L between a di-pion state and the third pion. The
a2meson decays into rrf r- n ’ through the
p*.rrTintermediate states with constructive interference
[161;
par’ is forbidden by isospin in- variance. For the decay of a candidate high-mass resonance, the intermediate states
p * T ’and f2ro are considered. The angular distribution depends on the spin-parity and helicity of the resonant state X [17,18]. It is given by
F=CR,
T,(X+p+K+37r)
2 2
h mp -
m2ll- im, r,+ T(X+p-rr++37r)
2 2
5 -m2?r- im, r, I
Th( X +f2m” -+
3~)
2
+ crexp( i4)
m;2 - m2,, - imf2 rf2 3 (1)
where
R,is the probability of the helicity A state,
rn2* is the invariant mass of the di-pion systemT?z?i E ~e~~e~h~~
of the fir and
prdecay amplitudes. For the a2, CY = 0. The transition amplitude
T,is given by
where rx is the X decay width at the resonance invariant mass
Wvu, mxis the resonance pole mass.
The product of the spherical harmonics (Y > is multi- plied by the Clebsch-Gordan coefficients (C). The di-pion system has spin 1 with third component
m,the mass dependent width is r,,.
The momentum, polar and azimuthal angles
(pzn,O,,,&,> are mea-sured in the yy rest frame. The r from the di-pion decay has the corresponding variables
(p,,,B,, , 4,)measured in the di-pion rest frame. The angles in both frames are determined with respect to the y-y direction which is approximately the beam direction.
The mass-dependent widths of the
a2, f2and
p aregiven by Ref. [19]. Spin-parity Jp = l* and J’(A) = 2-(2) are excluded by the Landau-Yang theorem [20], and a Jp = O+ state cannot decay into 3~ by parity conservation.
2.
Event selection and background estimationsThe process e’e-+ e’e-~‘~-n ’ has been selected in an untagged configuration. The
pTthreshold for charged track selection is 60 MeV. The energy of a photon candidate is required to be greater than 80 MeV with an angular separation from charged tracks of (AtI + Ac$‘Y’~ > 5.5”. Photon candidates are selected in the angular regions 14” < 8 < 35”,
m(dC”)
[GeV]Fig. 1. The T+T-T’ invariant mass spectra for IEprlz below a) and above b) 0.0015 GeV’.
M. Acciarri et al. / Physics Letters B 413 (1997) 147-158
1.0<m(xfn~no)<1.55 GeV
2.1<m(n+Cn")<2.5 GeV I
Fig. 2. The IEprl* distributions for rr+n-rr’ events (points with statistical error) in different intervals of invariant mass. The IEprI* distributions are fitted to background of second order polynomial (dashed line) and Monte Carlo predictions (dotted line) in b) and c) for exclusive resonance formation. The shaded histogram in c) is the distribution for a rr+n-rr”(no) phase space Monte Carlo sample normalized to the polynomial background estimate.
45"< 8< 139, or 145" < 8< 166". The rr” signal region is defined as 105 < m( yy) < 165 MeV, where m(yy) is the invariant mass of the two photons.
The transverse momentum of the 7~’ 7~~ rr ’ sys- tem relative to the beam direction is denoted by Cp,. The mass spectra with ICprl* below and above 0.0015 GeV* are shown in Fig. 1. The distri- bution is dominated by the u2. One sees that the mass resolution deteriorates and the background in- creases at higher values of ICpr[*. Fig. 2a to 2d show the
ICpr I*
distributions for different 7~+ nr- 7~’mass intervals. In the mass intervals 1.0-1.55 GeV and 1.55-2.1 GeV there is a clear excess of events at
m(m) [GeV]
Fig. 3. rr *no (two entries per event) and n+niT- mass distribu- tions for selected n+n-rr’ events. The arrow indicates the cut applied to rr *no to define the low-mass sample.
low ICpT12 corresponding to exclusive rrf W 7~’
production. The almost flat background extending to large ICprl* values is interpreted as inclusive pro- duction. The shaded histogram in Fig. 2c shows the prediction of a Monte Carlo phase space generation of the channel rr+ rr- rr ‘(,rr ‘> where the last 7~’ is unobserved. This describes correctly the shape of the distribution for large
ICpr I’.
To estimate the statistical significance of the ex- clusive signals several fits were performed to the ICp,l* distribut’ ions below 0.02 GeV*. The results and confidence levels of “background only” fits to a second order polynomial are given in the first two
Table 1
The ICpr1’ distributions below 0.02 GeV’ in the four mass ranges are fitted to background only (first two rows) and Monte Carlo plus background (third and fourth rows). The x’ for 130 D.F. are listed. The fraction of background events in IEprl’ <
O.O015GeV* are also listed with the number of events observed mass region [GeV] 0.60-1.00 1.00-1.55 1.55-2.10 2.10-2.50
x ’ (Background) 105 585 221 92
C.L.[%l 95 <lo-6 1.1x10-4 99
x2 (MC+
Background) C.L.[%l
_ 157 155 _
_ 5.4 6.7 _
Total events 42
Background events _ Background fraction - [%I
618 184 38
120 46 -
19+0.5 25+3 _
M. Acciarri et al./ Physics L&ten B 413 (1997) 147-158 153
rows of Table 1. To estimate the levels of the inclusive backgrounds under the exclusive produc- tion signals in Figs. 2b,c the distributions were fitted to the sum of a Monte Carlo distribution including the effect of a p dominated Vector-Meson-Domi- nance (VMD) form factor to describe the exclusive signal, and a second order polynomial to describe the inclusive background. As listed in the third row of Table 1, acceptable fits are then obtained. The back- ground levels for ICpr1’ < 0.0015 GeV2 of the fits are listed in the last three rows of Table 1.
In the spin-parity-helicity analyses presented be- low, events with ICpr12 < 0.0015 GeV2 are divided into two samples. The a2
low-masssample is se- lected with r’ r- r ’ invariant mass of 1.0 <
m(r+Kn’)<1.55 GeV. The ~*:‘TT’ invariant mass is required to be compatible with the p mass
(m(r * TO) < mp +250 MeV) since the a2 decays predominantly through the
piintermediate state (see Fig. 3). The
high-masssample of 1.55 <
m(rr’ nTT- TO) <
2.1 GeV is studied under the hy- pothesis of a resonance (or resonances) decaying through
prand f2r.
The detector acceptance and event selection effi- ciency for different spin-parity and helicity states have been evaluated by Monte Carlo simulations using the PC [21] and TWOGEN [22] generators with a
pdominated VMD form factor applied for the colliding photons. The mass and total width for the a2 are taken from the Particle Data Group (PDG) [12]. In the high-mass range a Breit-Wigner reso- nance of mass 1740 MeV and total width 150 MeV have been assumed. Monte Carlo events were passed through a full detector simulation. The detector ac- ceptances for ICpr12 < 0.0015 GeV 2 calculated for different intermediate states and spin-parity assign- ments are listed in Table 2. For the high-mass region the amplitude and phase parameters CY and 4 deter- mined by the fits described in Section 3 below are used.
Table 2
The detector acceptance _M for events with lEpr12 < 0.0015GeV2 of different spin-parity-helicity states and Lorentz invariant phase space (LIPS)
a&320) + pi BW(1740) + ,XT + firr
J’(A)
2+ (0) 2+(2) LIPS 2- (0) 2+ (0) 2+(2) LIPS.M
181
0.41 0.50 0.42 0.72 0.63 0.91 0.583. Spin-parity and helicity analysis
We have analyzed the low-muss sample to obtain the helicity state of the
a2.When produced in quasi- real two-photon collisions, the u2 meson can have helicity states 0 or 2. The relative importance is determined by the least square minimization to the polar angle
(cos 0)distributions of the final state pions in the resonance rest frame where 8 = r - 8,, . The case distributions are sensitive to the helicity state. The Monte Carlo expectations for the cos0 distributions of 7~’ and r * (two entries per event) are given by
Ei = Pb.gi
+ PYY .IP2.M;(2)+(1-P2).M,cO>} (3)
where M,(h) is the bin content of simulated events of helicity A normalized to the expected number of events for a radiative width rYy = 1 keV. The back- ground distribution 9: is taken from the rTT+ 7~~ 72 ’ phase space Monte Carlo. The free parameters in the fit are the fraction
P,of helicity 2 contribution, and the two scaling factors
P,,,,for the radiative width of the resonance and
P,for the background contribu- tions. The
P2parameter corresponds to
R,in Eq.
(1) (P,/(l - P2) = R,/R,). The
forward regions (Icos8l> 0.94) with low acceptance are excluded from the tit. The result of the fit is shown in Fig. 4.
We have obtained
Pyy = 0.96 f 0.04 and P, = 0.92 f 0.05 with x2/D.F. = 90/53 (C.L. = 0.11%). The Pbobtained corresponds to 26 + 2% of background contamination, which may be compared with the estimated level of inclusive background of 19.0 + 0.5% obtained from the fit to the ICpr12 distribution.
The excess of 7% of events is used to estimate the rate of s-wave nt n- no production (possibly rr(1300) formation). It corresponds to 41 observed events which implies a radiative width of
&BR(r+ rTT- TO) <
0.085 keV at 90% CL. for any s-wave contribution.
The fitted parameters are sensitive to the back-
ground level. We performed the fit again with the
background fraction fixed to 20%. The parameters of
the fit are in this case
P,, =1.05 + 0.03 and
P, =154 M. Acciarri et d/Physics Letters B 413 (1997) 147-158
I\ 60 a\ To p+(o)
case
Fig. 4. cos0 distributions of a) TO and b) IT * (two entries per event) for az (points with statistical error) which are compared to the results of the fit (solid line). The dotted and dashed lines indicate the contributions for the two helicity states and the shaded area represents the background.
0.87 + 0.05
with x’/D.F. = 90/54 (C.L. = 0.15%).The total systematic uncertainty in
P,
is estimated to be 6% and has dominant contributions from back- ground uncertainty and detector acceptance, each estimated to be 4%.In the high-mass sample we observe 184 events.
The intermediate decay modes pn- and f2m are considered for the exclusive signal. The coherent interference of the two intermediate states pr and
f2r
is expressed in Eq. (1). We first analyze the spin-parity state using the Dalitz A parameter [23]defined in the mf m- 7r ’ rest frame by
A=
P,+XP,- 2
I I Qi (4
where the 7~ k momenta (p, .> are normalized to QK, the maximum possible kinetic energy for a pion
in the event. The A distribution is shown as the data points in Fig. 5.
The Dalitz A parameter is sensitive to the distri- bution of the relative angles between the final state pions, and depends on the spin-parity of the state as well as the amplitude and phase parameters (Y and 4. We compare data with Monte Carlo event sam- ples generated with different values of the (Y and 4 parameters for each spin-parity-helicity state. A background level of 25% of inclusive events, as determined by the fit to the (Cpr12 distribution (Fig.
2), was used. The background is simulated by Monte Carlo r’ 7~~ ,rr”(,rro) phase space events. Increasing either of these parameters in the Monte Carlo shifts the A distribution to lower values. The parameters (Y and 4 are determined for each spin-parity and helic- ity state by minimizing the x2 value. The results of the fits are listed in Table 3. For both 2+(O) and 2+(2) the fitted value of (Y is consistent with one. In all cases the phase angle is large (> 90”) and for 2+(2) is consistent with 4 = 180” (f2r and pr amplitudes relatively real). No acceptable fit was found for 2-(O). The spin-parity Jp = 2+ is strongly favored. This fit is not, however, sensitive to the helicity state.
Comparisons are also made for different a and 4 values with the effective mass spectra of the interme- diate rr * 7~’ and r+rTT- states. The mass peak
Fig. 5. A distribution of data (points with statistical error) and Monte Carlo of J’(A) = 2+ (0) (dotted), 2+ (2) (solid), and 2- (0) (dashed). respectively. A 25% inclusive background (shaded) is included using a phase space T+T-T’(T’) distribution.
h4. Acciarri et al./Physics Letters B 413 (1997) 147-158 155
M(m) [GeV]
Fig. 6. a) n *no (two entries per event) and b) rr+n- mass spectra in comparison with Monte Carlo predictions that contain 25% inclusive ~+Yn’(n’) background events (dashed line).
positions also move as the phase angle increases; the r*r” mass toward lower values and the r+ w mass in the opposite direction. The (Y and $I param- eters determined are consistent with those obtained from the A distributions. The di-pion mass spectra of the intermediate states are shown in Fig. 6 in comparison with the Monte Carlo predictions for different Jp( A) assignments.
The helicity state can be 0 or 2 as for the a2 with different angular distributions in the rTT+ w rr ’ rest frame. Fig. 7 shows the cos6’ distributions for no and r * (two entries per event). The data is fitted to Monte Carlo expectations of pure 2-(O), 2+(O), 2+(2) states and inclusive rr+ n- .sr”(no> back- ground:
Ei = Pb.9~
+Py;{(l -F2-)[P*Yw
+(1 - P,)M:(o)] +F,-&f-(0)}. (9
Table 3
Results of fits to the A distribution
JP(A) 2- (0) 2+ (0) 2+c21
phase angle I#J [den.] _. _ 100 130* 18 170+ 17
amplitude o 1.0 0.99kO.10 0.97+0.17
x*/15 D.F. 3.94 0.83 0.61
CL. [%I 3.6x 10m5 64 a7
The inclusive background is parameterized by 9:
and scaled by Pb. P,,, and P2 are defined as in Eq.
(3). The parameter F,- is the relative contribution of the 2-(O) state. The results of the fits are listed in Table 4. Assuming a pure 2-(O) state gives a low CL. of 1.7 X lo-* (column I). The fitted values of the background level and P2 are 23 & 4% and 77 f
12% respectively (column II). The fitted background is consistent with that derived from the ICpr[’ distri- butions (25 + 3%, Table 1). A fit is also performed with background level fixed at 23% and the 2-(O)
Fig. 7. costi distributions of a) no and b) n * (two entries per event) for the high-mass selection (points with statistical error) which are compared to the results of the fit (solid line, column II of Table 4).
156 M. Acciarri et al./ Physics Letters B 413 (1997) 147-158 Table 4
Parameters of fits to cos0 distributions of no and v *. (* ) parameter fixed in the tit
Background [%I P, 141 2 - (0) [%I PYI [kevl C.L. [%I
I II III
0* 23+4 23’
_ 77+12 74+13
100’ 0” 12*11
0.43 + 0.02 0.38 f 0.03 0.39 F 0.02
1.7x 10-6 57 61
contribution left free (column III). The upper limit for a possible 2- (0) contribution is r,,
X BR(rr+ 7r- ,rr’) I 0.072 keV (90% C.L.).
The systematic errors in P, given by uncertain- ties in detector acceptance, background levels, and the uncertainty in the
pr/f2r
branching ratio are estimated to contribute 4% each, for a total of 7%.4. Resonance parameters
The rn(r+ rTT- TO> mass spectrum in the region 1.0-2.1 GeV with ]Cpr1* < 0.0015GeV2 is fitted by minimizing a x2 function with expected value in bin i of:
Ei = r,y . Mi”’ + BWi + P&8;. (6) The a, contribution, represented by Mf?, is given by the Monte Carlo, assuming the PDG average values of the mass and width [ 121, and helicity 2 fraction P, = 0.92, as determined in Section 3 above. The a2 contribution is scaled by the factor r,“;, which is a free parameter in the fit. The high-mass exclusive signal is described by the Breit-Wigner function:
r
BW= P,, . tot
(m* - Wy’y)’ + m2rt,2, ’
(7)
with fit parameters P,,, rtot and m. The detector acceptance is folded in P,,. The inclusive back- ground .Q?y is estimated from the fits to the ]Cp, I*
distributions shown in Fig. 2. The shape is parame- terized by a third order polynomial with the normal- ization P, left free in the fit. The result of the fit is shown in Fig. 8, with x2 = 57 for 42 D.F. (C.L. = 6.1%).
The radiative widths for a2 and the events in the high-mass region described by Eq. (7) are obtained from the fitted parameters rYq2 and P,,. The nor-
malization factor P, of the background obtained from the fit is 0.94 f 0.10, which is consistent with the level estimated from the ICpr
I*
distributions.The fitted widths are rYy = 0.98 k 0.05 for the a2 and r,, BR(QT+ T- TO> = 0.29 f 0.04 for the high- mass region assuming a single resonance. For the u2, the radiative width is consistent with that obtained from the angular distribution (Section 3). The sys- tematic errors in the radiative widths are due to uncertainties in acceptance, background, and branch- ing ratios. For the a2 these contributions are 3%, 4%
and 7%, respectively; while for the high-mass region they are 4% for acceptance and 4% for background.
These values are summarized in Table 5.
The fitted resonance parameters are corrected for the calibration estimated by the Monte Carlo simula- tions. The mass-dependent width introduces a mass shift of -11 + 1 MeV at m = 1320 MeV and -20
k 2 MeV at m = 1750 MeV. The photon energy and track momentum measurements both have a slight offset to lower values of the order of l%, which are determined by the effective mass distributions of inclusive 7r” --) yy and K, + rr+
rr- ,
respectively.-20h
rn(x%?)
[GeV]’
Fig. 8. a) r’nX-rO invariant mass spectrum; the solid line is the tit to the Monte Carlo sample for the a2 (dotted line), a Breit- Wigner distribution in the high-mass region (dotted-dashed line) and a background parameterized by a third order polynomial (dashed line). b) the distribution with az and background sub- tracted.
M. Acciarri et al. / Physics Letters B 413 (1997) 147-158 157 Table 5
The resonance parameters and the corresponding statistical and systematic errors
a&320) High-mass region rY, IkeVl 0.98 f 0.05 + 0.09 _
ryY BR - 0.29 + 0.04 f 0.02
(PP +J$Tr) I keV1 m [MeV]
r [MeV]
p, [%I
1323 f 4 f 3 1752 + 21 + 4 105 * 10 + 11 150+110&34
92+5*5 77j,12+5
The combined offsets for rr+ rTT- r ’ are estimated by the Monte Carlo to be - 2 k 3 and - 12 f 3 MeV at 1320 and 1750 MeV, respectively. The systematic uncertainty is the combined error of the two shifts.
For the high-mass region the corrected mass is m = 1752 &- 21 f 4 MeV. We also made a separate Breit-Wigner fit for the mass and width of the u2.
The mass is found to be 1323 k 4 k 3 MeV. The mass resolution of the detector increases the r val- ues obtained in the Breit-Wigner fits. This effect is calculated using Monte Carlo. The corrections to r are -38 + 11 MeV and -60 f 34 MeV for the a, and at 1750 MeV, respectively; the corrected widths are r= 105 + 10 f 11 MeV and r= 150 f 110 + 34 MeV, respectively.
The resonance parameters and the relative impor- tance of the helicity 2 state (P,) (Section 3) in the two mass regions are summarized in Table 5. The large error on the fitted width for the high-mass region and the apparent excesses of events relative to the fitted curve around 1.5 GeV and 1.85 GeV indicates that the single Breit-Wigner fit should be considered only as a rough description of the data in the high-mass region.
5. Discussion and conclusions
The rTT+ 6 T ’ final state in two-photon collisions is found to be dominated by formation of the a2 meson. The resonance mass and total width and radiative width (Table 5) obtained are in good agreement with the current world average values [12]. The A = 2 helicity state is dominant. A upper
limit for s-wave contribution is estimated to be r,,
BR(r+ mTT- TO) <
0.085 keV (90% C.L.).The 7~~rr-r’ events in the high-mass region (1.55-2.1) GeV have been analyzed for spin-parity and resonance parameters for spin up to J = 2 and in intermediate states prr and f2n. From the analysis of the A parameter distribution and the pion cos6’
distributions, the spin-parity of the selected exclusive events are found to be dominated by J’(h) = 2+(2).
Equal branching ratios for decays into the fir and pm final states are observed and the phase angle 4 between the pn and fzn amplitudes is consistent with 180”. The results may be compared with theo- retical predictions, in particular the calculations of the relativistic quark model of Ref. [14]. If these events are identified with the first radial excitation of the u2, the fitted mass m = 1752 f 2 1 + 4 MeV is consistent only with the One Gluon Exchange Semi- Relativistic Quark Mass (OGE-SRM) model which predicts a mass of 1740 MeV. All the models of Ref. [ 141 give values of rYy(d2) in the range 0.33-0.38 keV, compatible with our measurement l&
BR(T+T-T') = 0.29 + 0.04 f 0.02
MeV,onthe assumption that 37r decay mode is the dominant one.The presence of several overlapping states in the high-mass region cannot be excluded. The OGE-SRM model predicts a second radial recurrence of the u2 at 1820 MeV where a small data excess is seen.
Higher statistics are needed to better understand this mass region.
The formation of a Jp = 2- state, 7~~) claimed by previous collaborations [lo,71 was based solely on the 3~ mass distribution and observation of f27r decay mode. No evidence is seen for this state. The upper limit
II,,,(T,)BR(T+T-TT~) < 0.072
keV (90% C.L.) is found. This result is in agreement with the ARGUS observation [9]. We conclude that the spin-parity of fl+ 7~~ n O final states in this mass region is actually dominated by Jp = 2+ with helic- ity A = 2. The measured two-photon width is consis- tent with the theoretical predictions [ 11,13,14] for a radially excited a, state.Acknowledgements
We wish to express our gratitude to the CERN accelerator divisions for the excellent performance of
158 M. Acciarri et al. / Physics Letters B 413 (1997) 147-158
the LEP machine. We acknowledge the contributions of all the engineers and technicians who have partici- pated in the construction and maintenance of this experiment.
I71 [81 I91 [lOI
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